Large solutions for equations involving the p-Laplacian and singular weights |
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| Authors: | Jorge García-Melián |
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| Affiliation: | (1) Department of Mathematics, The Australian National University, Canberra, ACT 0200, Australia;(2) Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Universit? degli Studi di Napoli “Federico II”, Complesso M. S. Angelo, Via Cintia, 80126 Napoli, Italy |
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| Abstract: | In this paper we consider the boundary blow-up problem Δpu = a(x)uq in a smooth bounded domain Ω of mathbbRN{mathbb{R}}^N, with u = +∞ on ∂Ω. Here Dpu = div(|?u|p-2?u)Delta_{p}u = {rm div}(|nabla u|^{p-2}nabla u) is the well-known p-Laplacian operator with p > 1, q > p − 1, and a(x) is a nonnegative weight function which can be singular on ∂Ω. Our results include existence, uniqueness and exact boundary behavior of positive solutions. |
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